Least Common Multiple of 1460 and 1464

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1460 and 1464 the smallest integer that is 534360 that is divisible by both numbers.

Least Common Multiple (LCM) of 1460 and 1464 is 534360.

LCM(1460,1464) = 534360

LCM of 1460 and 1464

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 1460 and 1464

LCM of 1460 and 1464 is 534360

Least common multiple can be found by multiplying the highest exponent prime factors of 1460 and 1464. First we will calculate the prime factors of 1460 and 1464.

Prime Factorization of 1460


2 1460
2 730
5 365
73 73
1

Prime factors of 1460 are 2, 5,73. Prime factorization of 1460 in exponential form is:

1460 = 22×51×731

Prime Factorization of 1464


2 1464
2 732
2 366
3 183
61 61
1

Prime factors of 1464 are 2, 3,61. Prime factorization of 1464 in exponential form is:

1464 = 23×31×611

Now multiplying the highest exponent prime factors to calculate the LCM of 1460 and 1464.

LCM(1460,1464) = 23×31×51×611×731
LCM(1460,1464) = 534360

Factors of 1460

List of positive integer factors of 1460 that divides 1460 without a remainder.

1, 2, 4, 5, 10, 20, 73, 146, 292, 365, 730, 1460

Factors of 1464

List of positive integer factors of 1464 that divides 1464 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 61, 122, 183, 244, 366, 488, 732, 1464

Least Common Multiple of 1460 and 1464 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1460 and 1464, than apply into the LCM equation.

GCF(1460,1464) = 4
LCM(1460,1464) = ( 1460 × 1464) / 4
LCM(1460,1464) = 2137440 / 4
LCM(1460,1464) = 534360

Properties of LCM 1460 and 1464

(i) The LCM of 1464 and 1460 is associative

LCM of 1460 and 1464 = LCM of 1464 and 1460

Related Least Common Multiples of 1460

Related Least Common Multiples of 1464

Frequently Asked Questions on LCM of 1460 and 1464

1. What is the LCM of 1460 and 1464?

Answer: LCM of 1460 and 1464 is 534360.

2. What are the Factors of 1460?

Answer: Factors of 1460 are 1, 2, 4, 5, 10, 20, 73, 146, 292, 365, 730, 1460. There are 12 integers that are factors of 1460. The greatest factor of 1460 is 1460.

3. What are the Factors of 1464?

Answer: Factors of 1464 are 1, 2, 3, 4, 6, 8, 12, 24, 61, 122, 183, 244, 366, 488, 732, 1464. There are 16 integers that are factors of 1464. The greatest factor of 1464 is 1464.

4. How to Find the LCM of 1460 and 1464?

Answer:

Least Common Multiple of 1460 and 1464 = 534360

Step 1: Find the prime factorization of 1460

1460 = 2 x 2 x 5 x 73

Step 2: Find the prime factorization of 1464

1464 = 2 x 2 x 2 x 3 x 61

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 534360 = 2 x 2 x 2 x 3 x 5 x 61 x 73

Step 4: Therefore, the least common multiple of 1460 and 1464 is 534360.